## Domain and Codomain

A function is an operationthat assigns to each number ina domain, a unique number ina codomain. The function is usually given in the form of an equation,for example, Eachvalue of givesa unique value of -if this were not so, we would not have a function. To sketch afunction we need to find a set of points. This is most easily done bydrawing up a table.

-3 | -2 | -1 | 0 | 1 | 2 | 3 | |

9 | 4 | 1 | 0 | 1 | 4 | 9 | |

+1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

10 | 5 | 2 | 1 | 2 | 5 | 10 |

If we have a graph of a function and we want to knowthe domain and codomain, then we can find them by looking at theaxes. To find the domain, we look at the x-axis. To find the range orcodomain we look at the-axis. For the function above, the function is restricted tovaluesin the rang [-3,3] so the domain is the interval, [-3,3] and thecodomain or range is the interval [1,10].

The graph below,hasdomain(noticethe vertical dotted line, indicating that atsocannotbe equal to -1) and codomainIfthe graph tends toward anorvaluewithout reaching it, then that value cannot be in the domain orcodomain respectively.